5x^2-10x^2=-7+x+x^2

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Solution for 5x^2-10x^2=-7+x+x^2 equation:


Simplifying
5x2 + -10x2 = -7 + x + x2

Combine like terms: 5x2 + -10x2 = -5x2
-5x2 = -7 + x + x2

Solving
-5x2 = -7 + x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -1x + -5x2 + -1x2 = -7 + x + x2 + 7 + -1x + -1x2

Combine like terms: -5x2 + -1x2 = -6x2
7 + -1x + -6x2 = -7 + x + x2 + 7 + -1x + -1x2

Reorder the terms:
7 + -1x + -6x2 = -7 + 7 + x + -1x + x2 + -1x2

Combine like terms: -7 + 7 = 0
7 + -1x + -6x2 = 0 + x + -1x + x2 + -1x2
7 + -1x + -6x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
7 + -1x + -6x2 = 0 + x2 + -1x2
7 + -1x + -6x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + -1x + -6x2 = 0

Factor a trinomial.
(1 + -1x)(7 + 6x) = 0


Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + 6x)' equal to zero and attempt to solve:

Simplifying
7 + 6x = 0

Solving
7 + 6x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x = 0 + -7
6x = 0 + -7

Combine like terms: 0 + -7 = -7
6x = -7

Divide each side by '6'.
x = -1.166666667

Simplifying
x = -1.166666667
Solution
x = {1, -1.166666667}

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